Nanofiber forests, composed of both single wall and multiwalled nanotubes, can be drawn into nanofiber ribbons or sheets. In its pre-drawn state, the nanofiber forest comprises a layer (or several stacked layers) of nanofibers that are parallel to one another and perpendicular to a surface of a growth substrate. When drawn into a nanofiber sheet, the orientation of the nanofibers changes from perpendicular to parallel relative to the surface of the growth substrate. The nanotubes in the drawn nanofiber sheet connect to one another in an end-to-end configuration to form a continuous sheet in which a longitudinal axis of the nanofibers is parallel to a plane of the sheet (i.e., parallel to both of the first and second major surfaces of the nanofiber sheet). Individual nanofiber sheets can be from a few microns thick to tens of nanometers thick. Nanofiber sheets can then be spun into nanofiber yarns.